Partition functions, mapping class groups and Drinfeld doubles

TL;DR

This paper constructs invariants of higher genus partition functions in 2D conformal field theories using Drinfeld doubles of finite groups, applicable across different fields and without semisimplicity assumptions.

Contribution

It provides explicit formulas for these invariants, extending previous work to a broader algebraic setting without characteristic or semisimplicity restrictions.

Findings

Explicit expressions for invariants of Drinfeld doubles

Invariants are independent of the underlying field's characteristic

Results do not require semisimplicity

Abstract

Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete expressions obtained for the case of Drinfeld doubles of finite groups. The results for doubles are independent of the characteristic of the underlying field, and the general results do not require any assumptions of semisimplicity.